/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 11 Someone claims that, since the m... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 11

Someone claims that, since the mean of the sampling distribution equals the population mean, any single sample mean must also equal the population mean. Any comment?

Short Answer

Expert verified
Individual sample means can vary from the population mean due to randomness and variability in sampling. While the mean of the sampling distribution (i.e., average of all possible sample means) equals the population mean, this doesn't imply every single sample mean will also equal the population mean.

Step by step solution

01

Understand the Concepts

Population mean refers to the average of all data points in a population. Sample mean refers to the average of a subset (or 'sample') of that population. When many samples are drawn from the same population, the mean of all these samples forms a 'sampling distribution.' The Central Limit Theorem states that the mean of this sampling distribution equals the population mean.
02

Clarify Misconception

This does not mean every single sample mean equals the population mean. In fact, due to randomness and variability in sampling, individual sample means can vary quite substantially from the population mean.
03

Example to Illustrate

For instance, consider a population of adult heights. While the population mean height may be 170 cm, an individual sample (e.g., a sample of basketball players) could result in a sample mean much higher than 170 cm.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Indicate whether the following statements are True or False. The mean of all sample means, \(\mu_{\bar{x}}, \ldots\) (a) always equals the value of a particular sample mean. (b) equals 100 if, in fact, the population mean equals 100 . (c) usually equals the value of a particular sample mean. (d) is interchangeable with the population mean.

Define the sampling distribution of the mean.

Imagine a very simple population consisting of only five observations: 2,4,6,8,10. (a) List all possible samples of size two. (b) Construct a relative frequency table showing the sampling distribution of the mean.

Specify three important properties of the sampling distribution of the mean.

(a) A random sample of size 144 is taken from the local population of grade- school children. Each child estimates the number of hours per week spent watching TV. At this point, what can be said about the sampling distribution? (b) Assume that a standard deviation, \(\sigma,\) of 8 hours describes the TV estimates for the local population of schoolchildren. At this point, what can be said about the sampling distribution? (c) Assume that a mean, \(\mu,\) of 21 hours describes the TV estimates for the local population of schoolchildren. Now what can be said about the sampling distribution? (d) Roughly speaking, the sample means in the sampling distribution should deviate, on average, about \(\quad\) hours from the mean of the sampling distribution and from the mean of the population. (e) About 95 percent of the sample means in this sampling distribution should be between \({ }^{\text {hours and }}\) hours.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.